Problem: Factor completely. $9-25x^2=$
Answer: Both $9$ and $25x^2$ are perfect squares, since $9=({3})^2$ and $25x^2=({5x})^2$. $9-25x^2 = ({3})^2-({5x})^2$ So we can use the difference of squares pattern to factor. ${a}^2 - {b}^2 =({a}+{b})({a}-{b})$ In this case, ${a}={3}$ and ${b}={5x}$ : $({3})^2 - ({5x})^2 =({3}+{5x})({3}-{5x})$ In conclusion, $9-25x^2=(3+5x)(3-5x)$ Remember that you can always check your factorization by expanding it.